Relaxation time estimation in surface nmr

ABSTRACT

Technologies including NMR relaxation time estimation methods and corresponding apparatus are disclosed. Example techniques may generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T 1  and T 2 * as a function of position as well as one-dimensional and two-dimension distributions of T 1  versus T 2 * as a function of subsurface position.

CROSS REFERENCE TO RELATED APPLICATIONS

Priority is claimed to U.S. Provisional Patent Application No.61/591,643, filed on 27 Jan. 2012, entitled “RELAXATION TIME ESTIMATIONIN SURFACE NMR,” the disclosure of which is incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The field of the invention is surface Nuclear Magnetic Resonance (NMR)technologies to measure NMR properties of subsurface fluids andformations, and to use measured NMR properties to estimate otherphysical properties of the subsurface.

BACKGROUND

NMR systems have been in use for many years and can be used to provideimaging and/or analysis of a sample being tested. For example, U.S. Pat.No. 6,160,398, U.S. Pat. No. 7,466,128, U.S. Pat. No. 7,986,143, U.S.patent application Ser. No. 12/914,138 and U.S. patent application Ser.No. 13/104,721 describe a variety of NMR technologies, and areincorporated herein by reference. Various different types of NMR includemedical NMR, often referred to as Magnetic Resonance Imaging (MRI), andsurface NMR for measuring properties of earth formations. While there issome overlap in the technologies that may be applied in MRI and surfaceNMR, the samples being measured and the environments in whichmeasurements are performed are different, leading to many differences inthe technologies applied.

In general, surface NMR measurement involves utilizing or generating astatic magnetic field within a sample volume, emitting one or moreelectromagnetic pulses into the sample volume, and detecting NMRresponses from the sample volume. In some cases, surface NMR measurementinvolves emitting multiple electromagnetic pulses in rapid successionand measuring the NMR responses between the electromagnetic pulses. Themeasured NMR responses provide useful information about the samplevolume.

Surface NMR measurements may be used to detect, for example, theabundance of hydrogen contained within an underground sample volume, andNMR relaxation times within a sample. Detected hydrogen abundance andNMR relaxation times may be used to characterize many properties offluid-bearing formations underground, such as the porosity, totalquantity of fluids, fluid composition, pore size, and permeability ofthe sample. Three types of relaxation times of interest are referred toin the art as T₂*, T₂, and T₁.

There is a need in the art for better surface NMR measurement apparatusand methods. In particular, improved technologies for estimating NMRrelaxation times as described herein will provide bettercharacterization of fluid-bearing formations underground.

SUMMARY

Technologies applicable to NMR relaxation time estimation are disclosed.NMR relaxation time estimation may comprise performing surface NMRmeasurement methods according to this disclosure, and using resultingNMR data to estimate relaxation times and formation properties.

Some example surface NMR measurement methods may comprise generating aset of multi-pulse acquisition sequences, each multi-pulse acquisitionsequence comprising a preparatory pulse, wherein said preparatory pulsemay be substantially identical in each of the multi-pulse acquisitionsequences in the set. The preparatory pulses in the pulse sequences maycomprise on-resonance pulses, adiabatic pulses, and/or composite pulses.

Each multi-pulse acquisition sequence may further comprise one or moreordered subsequent pulses following the preparatory pulse. A pulsemoment of an ordered subsequent pulse in at least one of the multi-pulseacquisition sequences in the set may be different from a pulse moment ofa same ordered subsequent pulse in at least one other of the multi-pulseacquisition sequences in the set.

Example methods may furthermore comprise using NMR response dataproduced from the set of multi-pulse acquisition sequences to estimateNMR relaxation times T₁, T₂*, and/or T₂ as a function of position,and/or to estimate one, two, or other multi-dimensional distributions ofT₁ versus T₂*, or other relaxation time combinations, as a function ofposition.

Some example surface NMR measurement apparatus may include, inter alia,surface NMR measurement hardware such as a computer/controller, dataacquisition devices, a voltage/current generator, transmit switching,signal receive electronics, and/or detection coils. The computer orother controller may be configured with surface NMR measurement controlcircuits or software configured to execute the surface NMR measurementtechniques disclosed herein. Some example NMR measurement dataprocessing apparatus may include a computer configured with NMR dataprocessing software configured to process NMR data gathered according tothe disclosed surface NMR measurement techniques to estimate relaxationtimes T₁, T₂*, and/or T₂ as a function of position, and/or to estimateone-dimensional, two-dimensional or other multi-dimensionaldistributions of relaxation times as a function of position as describedherein.

Further aspects and variations are discussed in detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features and attendant advantages of the disclosed technologieswill become fully appreciated when considered in conjunction with theaccompanying drawings, in which like reference characters designate thesame or similar parts throughout the several views, and wherein:

FIG. 1 illustrates an example acquisition sequence for a laboratorysaturation recovery experiment.

FIG. 2 is a block diagram illustrating an example surface NMRmeasurement apparatus.

FIG. 3 illustrates an example surface NMR acquisition sequence for asurface NMR “Pseudo Saturation Recovery”.

FIGS. 4A, 4B, and 4C illustrate three example types of preparatorypulses: on-resonance, composite, and adiabatic.

FIGS. 5A, 5B, and 5C illustrate example surface NMR acquisitions in“crush recovery” sequences.

FIG. 6 illustrates an example crush recovery CPMG sequence.

FIG. 7 is a flowchart illustration of example pre-processing and spatialinversion methods for data acquired using a crush recovery sequence.

FIG. 8 is a flowchart illustration of example processing methods forestimating T₁ and T₂* parameters following pre-processing and spatialinversion of crush recovery data.

DETAILED DESCRIPTION

Prior to explaining embodiments of the invention in detail, it is to beunderstood that the invention is not limited to the details ofconstruction or arrangements of the components and method steps setforth in the following description or illustrated in the drawings. Theinvention is capable of other embodiments and of being practiced andcarried out in various ways. Also, it is to be understood that thephraseology and terminology employed herein are for the purpose of thedescription and should not be regarded as limiting.

Technologies directed to NMR relaxation time estimation are disclosed.The attached figures illustrate, inter alia: surface NMR acquisitionmethods; techniques to estimate NMR relaxation times; and surface NMRapparatus. Example surface NMR acquisition methods may includegenerating a set of two or more multi-pulse acquisition sequences, eachof the multi-pulse acquisition sequences comprising an initialpreparatory pulse followed by one or more subsequent “depth sensitive”pulses. The preparatory pulses may have substantially identicalproperties across the set of multi-pulse acquisition sequences, whilethe pulse moments of the depth sensitive pulses may be varied in the setof multiple acquisition sequences. The term “substantially identical” inthe context of preparatory pulses having substantially identicalproperties, refers to having a difference equal to or less than 5% ofthe larger preparatory pulse. For example, on-resonance preparatorypulses with pulse moments of 10 Amp seconds (As) and 10.5 As would beconsidered “substantially identical” for the purpose of this disclosure.

Example techniques to estimate NMR relaxation times may includeprocessing techniques for processing NMR data acquired with disclosedsurface NMR acquisition methods. Acquired NMR data may be used toestimate NMR properties and relaxation times such as T₁ and T₂* as afunction of position as well as one-dimensional and two-dimensionalcovariance distributions of relaxation times as a function of position.Resulting estimates of the relaxation time properties of the subsurfaceand their spatial distribution can be used to estimate other propertiesof the subsurface, including pore size and permeability.

Example surface NMR apparatus may include hardware, control softwareand/or processing software to execute surface NMR acquisition sequencesand/or NMR data processing tasks. Surface NMR apparatus may beconfigured to generate pulse sequences with pulse types, pulse moments,amplitudes, time delays, relative phases, or other pulse propertiesaccording to the surface NMR techniques disclosed herein. NMR dataprocessing apparatus may be configured to use recorded NMR signals intechniques to estimate NMR relaxation times introduced above, namely, toestimate NMR properties and relaxation times as a function of positionas well as one-dimensional and two-dimensional covariance distributionsof relaxation times as a function of position. NMR data processingapparatus may also be configured to use resulting estimates ofrelaxation times of the subsurface and their spatial distribution toestimate other properties of the subsurface including pore size andpermeability.

The present disclosure appreciates that not all decay times provideequivalent sensitivity to pore size and permeability. In particular T₂*,which is often the most straightforward parameter to measure, is oftenmore sensitive to inhomogeneity in the background magnetic field than topore size or permeability. The relaxation time T₂ can also besignificantly affected by magnetic inhomogeneity. The relaxation timewhich is generally least sensitive to magnetic field inhomogeneity andis most sensitive to pore size and permeability is T₁; however, T₁ isgenerally a more challenging relaxation time to measure by surface NMR.

In some embodiments, methods according to this disclosure may constrainthe mathematical estimation of T₁ to yield more accurate values of theT₁ relaxation time. Methods according to this disclosure may incorporateinformation pertaining to the covariance of T₁ with other relaxationtimes, which can be used to improve the precision and interpretation ofrelaxation time estimates.

FIG. 1 illustrates an example acquisition sequence for a laboratorysaturation recovery experiment. The sequence illustrated in FIG. 1comprises two transmit operations 101 and 103, shown on the “transmit”line, wherein transmit operation 101 is followed by a receive operation102, and transmit operation 103 is followed by a receive operation 104,shown on the “receive” line. The transmit pulses 101 and 103 areseparated by a delay time referred to as τ_(d,j). A longitudinalmagnetization of a sample to which transmitted pulses are applied isillustrated underneath the receive line. FIG. 1 furthermore includes anexample saturation recovery curve can be generated by repeating theillustrated sequence of transmit and receive operations while varyingthe delay times τ_(d,j) between each jth pulse sequence.

In a laboratory NMR measurement, the characterization of decay times fora sample volume may be generally straightforward, providing for highprecision and accuracy. An example laboratory NMR measurement begins byplacing a sample of known volume containing a hydrogen-bearing fluid ina static magnetic field. At equilibrium with the static magnetic field,the hydrogen nuclei produce a net nuclear spin magnetization that isaligned parallel to the direction of the background magnetic field(along the “longitudinal” or z axis).

A coil or antennae may then be used to apply an oscillating magneticfield transmit pulse to the sample, for example in the first transmitoperation 101. The applied oscillating magnetic field is referred to asB₁ and in the case of an on-resonance pulse may be tuned to the Larmorfrequency of the hydrogen nuclei, referred to as f₀. The application ofB₁ causes the spins to rotate an angle α, which is proportional to thepulse moment q of the transmit operation. For an on-resonance pulsetransmitted at frequency f₀, q is given by the product of the B₁ fieldamplitude within the sample and the duration of the B₁ magnetic fieldproduced by the transmit pulse.

After the transmit pulse 101 is extinguished, the component of themagnetization in the sample that was rotated into the so-called“transverse plane” (perpendicular to the longitudinal axis), precessesabout the longitudinal axis generating a detectable NMR signal thatresonates at the Larmor frequency. The NMR signal may be detected andobserved in the first receive operation 102. The NMR signal following atransmit pulse is referred to as the Free-Induction Decay (FID) signal.The FID signal decays over time as magnetization in the transverse planesimultaneously loses coherence and recovers to equilibrium alignmentalong the longitudinal axis.

The effective transverse relaxation time T₂* describes thecharacteristic decay time of coherent magnetization in the transverseplan and can be observed directly as the decay time of the FID signal.The transverse relaxation time T₂ describes the characteristic decaytime of coherence magnetization in the transverse plane with eliminationor mitigation of static de-phasing in an inhomogeneous field. Thelongitudinal relaxation time T₁ describes the characteristic timerequired for the magnetization to recover to equilibrium along thelongitudinal axis. Because the state of the longitudinal magnetizationis not directly indicated by the decay FID signal, a multi-pulsemeasurement sequence may be used to quantify T₁.

The so-called “saturation recovery” method is illustrated in FIG. 1. The“saturation recovery” method starts with the system at equilibrium, withmagnetization of a sample aligned along the longitudinal axis (M_(z)=M₀)prior to the application of an initial “saturation” pulse, e.g., thefirst transmit operation 101 illustrated in FIG. 1. In the laboratory,the value of q for the saturation pulse may be set such that the B₁magnetic field produced by the saturation pulse induces a α=90 degreeflip of the magnetization across the entire sample volume; thusmagnetization of the sample is rotated into the transverse plane, andthere remains substantially zero longitudinal magnetization immediatelyafter the saturation pulse (M_(z)=0).

Following the saturation pulse, an FID signal may be observed at thefirst receive operation 102, and the longitudinal magnetization of thesample may begin to recover along the longitudinal axis withcharacteristic recovery time specified as T₁.

After a finite delay time τ_(d), a subsequent 90 degree pulse may beapplied, e.g., the transmit operation 103. This subsequent pulse acts torotate the magnetization of the sample which has recovered along thelongitudinal axis back into the transverse plane. A subsequent FIDsignal may be observed in a subsequent receive operation 104. Theobserved magnitude of the subsequent FID signal may substantiallyexactly reflect the magnitude of the longitudinal magnetizationM_(z)(τ_(d)) that had recovered to equilibrium prior to application ofthe subsequent pulse.

By repeating this sequence using a range of delay times, and recordingthe values of M_(z)(τ_(d)), a saturation recovery curve can be generatedthat reflects the recovery of the longitudinal magnetization as afunction of delay time. For example the sequence may be repeated M timeswhere the value of the delay time τ_(d,j) is varied in each jth-indexedsequence. An example saturation recovery curve is illustrated at thebottom of FIG. 1. Fitting the curve with an exponential ormulti-exponential function (e.g., by Laplace inversion) may provide anestimate of the T₁ relaxation time or T₁ relaxation time distribution.While methods such as illustrated in FIG. 1 may work in the laboratory,the real-world circumstances of surface NMR measurement in the fieldmakes it more difficult to estimate relaxation times, and in particularto estimate T₁, outside the laboratory.

FIG. 2 depicts an example surface NMR measurement apparatus according tothis disclosure. The example surface NMR measurement apparatus 200 mayinclude a computer 210, function generators 211, 212, AC voltage/currentgenerator(s) 230, transmit switch(es) 240, NMR sensor(s) 250, receiveswitch(es) 260, preamplifier(s) 270, and Analog to Digital (AD)converter(s) 220. The NMR sensor(s) 250 are illustrated as an inductioncoil. Computer 210 comprises measurement control module(s) 201 and dataprocessing module(s) 202. The NMR sensor(s) 250 may be positioned over aground surface 280, and a subsurface fluid 281 is shown under the groundsurface 280. An arrow representing an example direction of Earth'smagnetic field 282 is also shown.

In FIG. 2, the computer 210 may be coupled to function generators 211,212 by connections 213 and 214, respectively. The computer 210 may alsobe coupled to AC voltage/current generator(s) 230 by connection 215, totransmit switch(es) 240 by connection 216, to receive switch(es) 260 byconnection 217, and to AD converter(s) 220 by connection 222.Furthermore, function generators 211, 212 may be coupled to ACvoltage/current generator(s) 230 by connections 231 and 232,respectively. AC voltage/current generator(s) 230 may be coupled totransmit switch(es) 240 by connections 233 and 234. Transmit switch(es)240 may be coupled to both ends 241 and 242 of the induction coilimplementing NMR sensor(s) 250. The ends of the induction coil(s) 241and 242 may be coupled to receive switch(es) 260 by connections 261 and262, respectively. Receive switch(es) 260 may be coupled topreamplifier(s) 270 by connections 271 and 272. Preamplifier(s) 270 maybe coupled to AD converter(s) 220 by connection 221.

In general, with regard to FIG. 2, measurement control module(s) 201 maybe configured to perform NMR measurements according to this disclosureby appropriately controlling the various other illustrated components ofthe surface NMR measurement apparatus 200. For example, the variouscomponents may be operated to produce current pulses on the NMRsensor(s) 250, to thereby create NMR excitation pulses. Properties oftransmitted pulses, delay times between pulses, and any other aspects ofpulse sequences may be adjusted to produce sets of multi-pulseacquisition sequences according to this disclosure. The computer 210 maybe configured to produce a pulse by selecting a pulse phase, pulsemoment, and/or other pulse properties, and activating the ACvoltage/current generator(s) 230. The computer 210 may also beconfigured to establish appropriate delay times between pulses inmulti-pulse acquisition sequences. The computer 210 may be configured toselect a pulse phase for example by activating a function generator 211or 212 corresponding to a desired pulse phase, so that the selectedfunction generator 211 or 212 provides an input pulse phase to the ACvoltage/current generator(s) 230, which may then be amplified by the ACvoltage/current generator(s) 230 to produce a corresponding pulse on theNMR Sensor(s) 250. The computer 210 may also optionally be configured toclose one or more transmit switch(es) 240 when activating the ACvoltage/current generator(s) 230, and open the transmit switch(es) 240after activating the AC voltage/current generator(s) 230.

Surface NMR measurement apparatus 200 may also be configured to receiveand record NMR signal data received via the NMR sensor(s) 250. SurfaceNMR measurement apparatus 200 may be configured to receive and recordNMR signal data after one or more excitation pulses. In someembodiments, the computer 210 may be configured to close the receiveswitch(es) 260 after a pulse. The preamplifier(s) 270 amplify NMRsignals received via induction coil(s) 250. The AD converter(s) 220convert the received and amplified signals to digital NMR signal data,e.g. by sampling received NMR signals at a desired sampling rate, andthe computer 210 or other device equipped with storage media may beconfigured to store the resulting digital NMR signal data.

In some embodiments, the NMR data processing module 202 may beconfigured to process NMR measurement data, generated by operation ofthe measurement control module 201 and the various other components ofsurface NMR measurement apparatus 200. NMR data processing module 202may be configured to estimate NMR relaxation times as disclosed herein,e.g. as described in connection with FIG. 7 and FIG. 8. It will beappreciated that while the computer 210 may be configured to include NMRdata processing module 202, in some embodiments NMR measurements and NMRdata processing may be performed separately, e.g., by first performingmeasurements with system 200, then processing acquired NMR data at alater time and/or with a different computing device comprising NMR dataprocessing module 202, or by a human operator.

It will be appreciated that surface NMR measurement apparatus may beconfigured differently than illustrated in FIG. 2 in some embodiments.To recite just a few of the many possible configuration options,computer 210 may be programmed with software that controls thegeneration of pulse sequences and the acquisition of NMR data. A set ofdata acquisition devices may comprise devices configured generate thecontrol signals for the pulse sequences, such as function generators211, 212, and AD converter(s) 220 that receive, convert and/or recordNMR signals. The AC voltage/current generator(s) 230 may be configuredto generate one or more current pulses in the induction coil(s) 250 in atransmit mode, to induce a coherent precession of NMR spins in a samplevolume. Optional transmit switch(es) 240 may be configured to isolatetransmitter noise from the receive circuitry during a receive mode. NMRsensor(s) 250 may be arranged other than as induction coils, and may beconfigured in a variety of ways as described herein or as known or asmay be developed in the art. Optional receive switch(es) 260 may beconfigured to isolate the receive preamplifier(s) 270 from thepotentially large voltage on the NMR sensor(s) 250 during transmit mode.Optional preamplifier(s) 270 may be configured to amplify the detectedNMR signals prior to digitization by the AD converter(s) 220. Theoptional transmit switch(es) 240 and receive switch(es) 260 may compriseactive devices such as relays, and/or passive devices such as diodes.Optional tuning capacitors, not shown in FIG. 2, may be used in thetransmit mode to increase the transmitted current in the inductioncoil(s) 250, and/or in receive mode to increase the amplitude of the NMRsignal voltage across the terminals of the induction coil(s) 250.

In some embodiments, NMR sensor(s) 250 may comprise an array of coilscomprising one or more transmit coils, one or more receive coils, and/orone or more combination transmit and receive coils. For example, NMRsensor(s) 250 may comprise one transmit coil and multiple receive coils.NMR sensor(s) 250 may comprise one combination transmit and receivecoil, and multiple receive coils. NMR sensor(s) 250 may comprisemultiple combination transmit and receive coils. These and othermulticoil arrangements may be configured in some embodiments as will beappreciated. Multicoil arrangements may be useful for localization offluids in structure 280, as described for example in U.S. Pat. No.2,466,128, entitled “Multicoil Data Acquisition and Processing Methods,”issued Dec. 16, 2008, which is incorporated by reference herein.

Any combination of hardware and software that enables the acquisitionand processing of NMR signals is suitable to implement embodiments ofthis disclosure. An architecture to implement the disclosed methodscould comprise, for example, elements illustrated in FIG. 2, such as anAC voltage and current generator 230, a digital control systemimplemented at least in part by computer 210, a transmit switchingcircuit including transmit switch(es) 240, a receive switching circuitincluding receive switch(es) 260, a multi-channel receive circuitincluding, e.g., a plurality of induction coils in NMR sensor(s) 250,preamplifier(s) 270, a digital acquisition system including ADconverter(s) 220, a digital storage device which may be implementedwithin computer 210 or other digital storage device, and a digitalcomputer 210. The switching circuits may transition a system such as 200between a transmit-mode, when the coil(s) 250 are connected to thetransmit circuit, and receive-mode when the coil(s) 250 are connected tothe receive circuit.

In general, NMR measurements may be collected by transmitting one ormore pulses of alternating current through NMR sensor(s) 250. Thealternating current may be tuned to the Larmor frequency of hydrogennuclei, for example, and may generate a magnetic field in a subsurfacefluid 281 alternating at the Larmor frequency. The alternating magneticfield radiates into the subsurface fluid 281 and modifies the nuclearmagnetization state of hydrogen atoms present in subsurface fluid 281.The transmitted alternating magnetic field perturbs the magnetizationfrom equilibrium alignment in a static magnetic field, so that somecomponent of the nuclear magnetization rotates into the transverse “xy”plane. Once rotated from equilibrium, the magnetization relaxes overtime back to the equilibrium state over time, decaying from thetransverse plane and re-growing along the longitudinal axis. Therotation of the magnetization by the transmitted pulse(s) and subsequentrelaxation to equilibrium are described by the phenomenological Blochequations. The evolution of the magnetization under the Bloch equationsdepends on several variables including the amplitude of the transmittedfield, the duration and timing of the transmitted field, the phase ofthe transmitted field, the longitudinal relaxation time T1, FIDrelaxation rate T2*, and/or the spin-spin relaxation time T2 of thehydrogen nuclei under investigation. These aspects of NMR measurementmay be used in determining the various NMR properties described herein.

In surface NMR measurement of subsurface fluids, the Earth's magneticfield 282 may be utilized as the static background field and the B₁field may be generated by transmitting current through one or more wireloops 250 laid out on the ground surface. Commonly an on-resonanceexcitation pulse is used (i.e., transmitted at the Larmor frequency f₀).The resulting excitation and precession of the nuclear magnetization insubsurface fluids 281 induces a voltage on the same coil 250 oradditional coils, and the coil voltage may be recorded at computer 210as the received NMR signal.

In contrast to laboratory measurements, for which the B₁ field isuniform over the investigated volume, for surface NMR measurements inthe field the B₁ magnetic field varies over the subsurface volume (i.e.the B₁ magnetic field is always stronger closer to the coil). As aresult, there may be a distribution of the B₁ magnetic field amplitudeand thus, for an on-resonance pulse, a distribution of tip angles withinthe subsurface following the transmitted pulse. Fluids located at aparticular position in the subsurface exhibit a maximum amplituderesponse if the tip angle at that position is close to 90 degrees or 270degrees and a minimum amplitude response if the tip angle at thatposition is close to 0 degrees or 180 degrees. By increasing ordecreasing the product q of current I on the coil 250 during thetransmitting pulse and the transmitting pulse duration t_(p), thedistribution of tip angles α as a function of subsurface position may bevaried as well as the sensitivity of the measurement to fluids atvarying depths. The product q may be referred to as the pulse moment.The maximum excitation depth is a function of q: as the pulse moment isincreased, the maximum excitation depth is also increased. We use theterm “maximum excitation depth” of a pulse to refer to the depth belowwhich tip angle rotations resulting from the pulse are substantiallyless than 30 degrees, e.g., anywhere from 0 degrees to 15 degrees. Itwill be appreciated that any tip angle may be selected for the purposeof measuring maximum excitation depth. A mathematical inversion of therecorded data measured for different values of q may be used to estimatethe variation in NMR parameters as a function of depth.

In an example single-pulse NMR FID measurement scheme, a singleacquisition sequence may comprise transmitting one on-resonance pulsewith finite duration t_(p) and a current I on a surface loop and thenrecording the subsequent NMR FID signal as one or more voltagemeasurements. A complete data set may comprise a collection of N singleacquisition sequences, where the value of q is varied between each ithacquisition sequence. The magnitude of I may be varied, and the durationof the pulse, t_(p), may also be varied to vary q. Identical singleacquisition sequences may be repeated to increase the signal-to-noiseratio.

The NMR voltage V(t,q) measured in the coil as a function of time and qcan be expressed in a forward model as the product of the spatialdistribution of water content and T₂* decay behavior at each subsurfacelocation r, and a kernel K(r,q) that represents underlying NMR physics,parameters of the coil geometry, parameters of the transmitted pulse,and other known parameters. A mathematical spatial inversion of the datacollected by such a single-pulse scheme, using the aforementioned model,yields the estimated NMR response from each subsurface volume element,reflecting the total longitudinal magnetization existing prior to thepulse (proportional to water content) and the T₂* decay behavior of thefluid associated with this longitudinal magnetization. The resultingestimates of water content and T₂* decay behavior as a function ofsubsurface position can be used to estimate other properties of thesubsurface formation, including pore size and permeability. However, theFID relaxation time T₂* may be less sensitive to pore size andpermeability than the relaxation time T₁.

FIG. 3 illustrates an example NMR acquisition sequence for NMR PseudoSaturation Recovery (PSR). PSR may provide an approach to measuring T₁by NMR which attempts to reproduce the saturation recovery experiment,described above for the case of laboratory conditions. FIG. 3illustrates a set of multi-pulse acquisition sequences includingacquisition i 300 and acquisition i+1 310. Acquisition i 300 may beperformed first, and acquisition i+1 310 may be performed next. Eachacquisition sequence comprises transmit operations illustrated on atransmit line and receive operations illustrated on a receive line.

In acquisition i 300, a transmit operation 301 is followed by a receiveoperation 302, there is a delay time τ_(d) between transmit operations,and a subsequent transmit operation 303 is followed by a subsequentreceive operation 304. Transmit operations 301 and 303 have a pulsemoment q_(i).

In acquisition i+1 310, transmit operation 311 is followed by receiveoperation 312, there is a delay time τ_(d) between the transmitoperations, and a subsequent transmit operation 313 is followed by asubsequent receive operation 314. Transmit operations 311 and 313 have apulse moment q_(i+1). FID signals FID1 are received in receiveoperations 302 and 312, and FID signals FID2 are received in receiveoperations 304 and 314. FID1 and FID2 may be different in the differentreceive operations 302, 312, 304, and 314.

In a basic PSR measurement scheme, a single acquisition sequence maycomprise transmitting two on-resonance transmit pulses, such as 301 and303, separated by an adjustable delay time τ_(d). In each singleacquisition, the two transmit pulses may have substantially the sameq-value. The FID signal following the subsequent transmit pulse (“FID2”)may be recorded; the FID following the first pulse (“FID1”) may also berecorded. An individual delay time data set may comprise of N singleacquisition sequences wherein the value of q for the two transmit pulsesis varied between each ith acquisition in the set and the value of τ_(d)remains fixed. A complete PSR dataset may comprise M multiple individualdelay time datasets between which the value of τ_(d) is varied betweeneach jth-indexed acquisition.

While the PSR dataset V(t, q, τ_(d)) may be sensitive to the T₁recovery, the PSR dataset V(t, q, τ_(d)) may be inadequate to quantifythe spatial variation in T₁ behavior in the subsurface. This is in partbecause the kernel that describes the PSR voltage signal in a forwardmodel is a function of T₁; thus, the mathematical inversion isnon-linear and poorly conditioned. In light of this complication, thefollowing simplifying assumptions might be made: (i) within thesubsurface volume contributing to the signal, the preparatory pulse isassumed to produce substantially a 90 degree tip angle and zerolongitudinal magnetization; (ii) the signal following the subsequentpulse only reflects the magnitude of the longitudinal magnetization therecovers during the delay time. As such, the PSR experiment may beapproximated as an ideal saturation recovery experiment. However, thisapproach may have limited validity and certain drawbacks describedbelow.

In fact, the above listed simplifying assumptions are generally at leastpartially invalid for the PSR dataset because both on-resonance pulsesin each double-pulse sequence actually produce a range of tip angleswithin the subsurface. For volumes in which the tip angle is far from 90degrees, a residual portion of the magnetization will be left along thelongitudinal axis following the first pulses, and the longitudinalcomponent will be non-zero. This residual magnetization will be excitedby the subsequent pulses into the transverse plane; thus, such volumeswhere the tip angle is far from 90 degrees will contribute to the signalfollowing the subsequent pulses that is associated with magnetizationthat has undergone T₁ recovery. As a result, the use and interpretationof PSR data can lead to errors in estimated values of T₁.

In addition to a need for improved determinations of T₁, NMRmeasurements may be improved by methodology for utilizing sensitivity ofthe measurement to the covariance of the T₁ and T₂* relaxation times ina geologic formation. Covariance of different NMR relaxation times canbe exploited to improve the characterization of subsurface formations.For example, dense sampling of one relaxation time can be used toimprove the resolution of a subsequent relaxation time. Further, thetwo-dimensional relaxation time distribution derived from atwo-dimensional inversion of relaxation times can provide more detailedinformation about the properties of the subsurface formation and fluidcontained therein. For surface NMR, T₁ and T₂* may show significantcovariance and this covariance may be exploited to provide additionalconstraint for the data inversion and more detailed characterization ofthe geologic formation. Thus in some embodiments, methodologies may usetheoretically bounded covariance of T₁ and T₂* to constrain and provideimproved estimation of relaxation time magnitudes. For example, it isknown that T₂* is never longer than T₁, and this may be used (amongother theoretically established covariance properties) to constrainestimation of T₁. In some embodiments, estimated covariance of T₁ andT₂* can be used to provide more detailed characterization of ageological formation than T₁ or T₂* alone.

The methods described in connection with FIG. 1 and FIG. 3 useon-resonance pulses and do not take advantage other pulse types or pulsesequence properties, described below, that may be useful for surface NMRmeasurements. Other pulse types and pulse sequences included in thepresent disclosure are illustrated in FIGS. 4A, 4B, and 4C, FIGS. 5A,5B, and 5C, and FIG. 6.

FIG. 4A illustrates properties of an on-resonance pulse. FIG. 4Billustrates properties of a composite pulse. FIG. 4C illustratesproperties of an adiabatic pulse. In an on-resonance pulse asillustrated in FIG. 4A, the current amplitude I(t), phase φ(t), andfrequency f(t), may be held constant over the duration of the pulse. Ina composite pulse as illustrated in FIG. 4B, the phase and/or theamplitude of the pulse may be changed between two or more discreteintervals of the pulse, e.g., from a value of I₀ to a value of I₁ andfrom a value of φ₀ to a value of φ₁. In an adiabatic pulse asillustrated in FIG. 4C, the amplitude of the pulse and/or the frequencyof the pulse may be varied continuously over the duration of the pulse.For example, I(t) may be varied from 0 to a maximum value of I_(max) asthe frequency is varied from an off-resonance value of f_(off) to theon-resonance Larmor frequency f₀.

By selecting appropriate functions for I(t), φ(t), and f(t), compositeand adiabatic pulses can produce tip angles in subsurface volumesunderneath NMR surface coils that may be substantially uniform over awider range of B₁ field strength, and thus may be substantially moreuniform over a wider range of distances from the surface coil, than maybe achieved using standard on-resonance pulses. For example, compositeand adiabatic pulses can be designed to produce tip angles that areclose to 90 degrees over a wide range of depths (e.g. adiabatichalf-passage) or 180 degrees over a wide range of depths (e.g. adiabaticfull-passage).

While on-resonance pulses may be distinguished from other on-resonancepulses by differences in pulse moment, composite and adiabatic pulses donot have a single pulse moment value. That said, “effective” pulsemoment values may be calculated to distinguish composite pulses fromother composite pulses, and adiabatic pulses from other adiabaticpulses. Another way to distinguish on-resonance, composite, andadiabatic pulses is by maximum excitation depth. The maximum excitationdepth of an on-resonance pulse, a composite pulse or and adiabatic pulseis generally a function of I(t), φ(t), and f(t) for the pulse. Themaximum excitation depth of a composite pulse or and adiabatic pulse isalso generally less than the maximum excitation depth of an on-resonancepulse with an equivalent value off ∫I(t) dt. This disclosure maytherefore refer to differences in maximum excitation depth or todifferences in pulse moment to distinguish between pulses in somecircumstances.

Improved Pulse Sequences

FIGS. 5A, 5B, and 5C illustrate example surface NMR acquisitions in“crush recovery” sequences. FIGS. 5A, 5B, and 5C illustrate a class ofacquisition sequences, which differ from the PSR acquisition sequenceshown in FIG. 3. Unlike the PSR sequence for which the preparatory pulsechanges between each ith acquisition, for the sequences shown in FIGS.5A, 5B, and 5C, the initial “preparatory” pulse may be substantiallyidentical between each ith acquisition, and the second or othersubsequent “depth profiling” pulse may be changed between each ithacquisition. Thus, the maximum excitation depth of the preparatory pulsemay be substantially identical for the set of N measurements with variedq₂.

FIG. 5A illustrates a NMR acquisition comprising a set of twomulti-pulse acquisition sequences for simplicity of explanation,understanding that sets may comprise any number of multi-pulseacquisition sequences. The multi-pulse acquisition sequences arereferred to as acquisition i 500 and Acquisition i+1 510. Each sequencecomprises transmit operations and receive operations.

During a transmit operation 501 of acquisition i 500, an on-resonancepreparatory pulse with pulse moment q₁ is transmitted. The transmitoperation 501 is followed by a receive operation 502 in which NMRsignals FID 1 are received. During a subsequent transmit operation 503of acquisition i 500, an on-resonance depth profiling pulse with pulsemoment q_(2,i) is transmitted. The subsequent transmit operation 503 isfollowed by a subsequent receive operation 504 in which NMR signals FID2are received.

Acquisition i+1 510 may be performed after acquisition i 500. As withacquisition i, during a transmit operation 511 of acquisition i+1 510,an on-resonance preparatory pulse with pulse moment q₁ may betransmitted. The transmit operation 511 may be followed by a receiveoperation 512 in which NMR signals FID 1 are received. During asubsequent transmit operation 513 of acquisition i+1 510, anon-resonance depth profiling pulse with pulse moment q_(2,i+1) istransmitted. The subsequent transmit operation 513 may be followed by asubsequent receive operation 514 in which NMR signals FID2 are received.

In FIG. 5A, the pulse moment q₁ of the on-resonance preparatory pulses501 and 511 (or the maximum excitation depth of the on-resonancepreparatory pulses) may be substantially identical in acquisition i 500and acquisition i+1 510. The pulse moments q_(2,i) and q_(2,i+1) of thedepth profiling pulses 503 and 513, however, may be substantiallydifferent. While any difference between depth profiling pulses 503 and513 may be usefully applied depending on the circumstances, someembodiments may comprise differences ranging between 0.5×, in which thelargest depth profiling pulse is 50% larger than the smallest depthprofiling pulse, and 10,000×, in which the largest depth profiling pulseis 10,000 times larger than the smallest depth profiling pulse. The term“substantially different” in the context of difference between pulsemoments of depth profiling pulses refers to any difference equal to orgreater than 0.5×, in which the largest depth profiling pulse is 50%larger than the smallest depth profiling pulse. Difference between depthprofiling pulses 503 and 513 in the general range of about 500×, inwhich the largest depth profiling pulse is about 500 times larger thanthe smallest depth profiling pulse may prove useful in many embodiments.It should be understood that in embodiments comprising manyacquisitions, there may be small differences between the depth profilingpulses of some acquisitions and larger differences between the depthprofiling pulses of other acquisitions.

Furthermore, in FIG. 5A, the pulse moment q₁ of the on-resonancepreparatory pulses 501 and 511, and thus the maximum excitation depth ofpulses 501 and 511, may be substantively different from the pulsemoments q_(2,i) and q_(2,i+1) of the depth profiling pulses 503 and 513.When the pulse moment q₁ of preparatory pulses 501 and 511 issubstantively greater than the pulse moments q_(2,i) and q_(2,i+1) ofthe depth profiling pulses 503 and 513, the maximum excitation depth ofpreparatory pulses 501 and 511 may be greater than the maximumexcitation depths of depth profiling pulses 503 and 513.

For the purpose of this disclosure, the term “substantively different”in the context of differences between pulse moments (or maximumexcitation depths) of preparatory pulses and pulse moments (or maximumexcitation depths) of depth profiling pulses refers to any differenceequal to or greater than 25% of the smaller pulse moment or smallermaximum excitation depth. In some embodiments, differences between pulsemoments (or maximum excitation depths) of preparatory pulses and pulsemoments (or maximum excitation depths) of depth profiling pulses may beequal to or greater than 50% of the smaller pulse moment or smallermaximum excitation depth. It is noted that using a single DC powersupply the transmission of a long pulse or long pulse sequence maydecrease energy stored on the power supply such that the bus voltagedecreases as energy is dissipated in the pulses, and the resultingpulses show a decreased amplitude (and therefore, decreased pulsemoment) as the energy is dissipated. Such decreases in pulse momentassociated only with pulse transmission and dissipation of power supplyenergy do not comprise a substantive difference in pulse moment as theterm is understood herein.

FIG. 5B illustrates a NMR acquisition in which the initial preparatorypulses are composite pulses, and as in FIG. 5A, described above, thepreparatory pulses remain substantially identical between each ithacquisition, while the subsequent (depth profiling) on-resonance pulsesmay be changed between each ith acquisition. FIG. 5B may generally beunderstood with reference to FIG. 5A, above. FIG. 5B comprises anacquisition i 520 and an acquisition i+1 530, wherein acquisition i 520comprises transmit operations 521 and 523 and receive operations 522 and524, and wherein acquisition i+1 530 comprises transmit operations 531and 533 and receive operations 532 and 534. In contrast with FIG. 5A,however, preparatory pulses 521 and 531 comprise composite, rather thanon-resonance pulses, which affects received NMR signals FID1 and FID2 ineach receive operation 522, 524, 532, and 534.

The composite preparatory pulses 521 and 531 may be designed withappropriate values of I(t), φ(t), and f(t) so that the maximumexcitation depth of the preparatory pulses 521 and 531 may be greaterthan or equal to the maximum excitation depth of the subsequent pulses523 and 533. In some embodiments, the maximum excitation depth of thecomposite preparatory pulses 521 and 531 may be substantively differentfrom the maximum excitation depths of the depth profiling pulses 523 and533. Preparatory pulses 521 and 531 may also differ qualitatively fromdepth profiling pulses 523 and 533 in some embodiments, e.g., when thepreparatory pulses 523 and 533 comprise composite pulses (with variedf(t) and I(t)) and the subsequent pulses 523 and 533 comprise resonancepulses (f(t)=f₀).

FIG. 5C illustrates a NMR acquisition in which the initial preparatorypulses are adiabatic pulses, and as in FIG. 5A, described above, thepreparatory pulses remain substantially identical between each ithacquisition, while the subsequent (depth profiling) on-resonance pulsesmay be changed between each ith acquisition. FIG. 5C may generally beunderstood with reference to FIG. 5A, above. FIG. 5C comprises anacquisition i 540 and an acquisition i+1 550, wherein acquisition i 540comprises transmit operations 541 and 543 and receive operations 542 and544, and wherein acquisition i+1 550 comprises transmit operations 551and 553 and receive operations 552 and 554. In contrast with FIG. 5A,however, preparatory pulses 541 and 551 comprise adiabatic, rather thanon-resonance pulses, which affects received NMR signals FID1 and FID2 ineach receive operation 542, 544, 552, and 554.

The adiabatic preparatory pulses 541 and 551 may be designed withappropriate values of I(t), φ(t), and f(t) so that the maximumexcitation depth of the preparatory pulses 541 and 551 may be alwaysgreater than or equal to the maximum excitation depths of the subsequentpulses 543 and 553. In some embodiments, the maximum excitation depth ofthe adiabatic preparatory pulses 541 and 551 may be substantivelydifferent from the maximum excitation depths of the depth profilingpulses 543 and 553. Preparatory pulses 541 and 551 may also differqualitatively from depth profiling pulses 543 and 553 in someembodiments, e.g., when the preparatory pulses 543 and 553 comprisecomposite pulses (with varied f(t) and I(t)) and the subsequent pulses543 and 553 comprise on-resonance pulses (f(t)=f₀).

In some embodiments, at least one multi-pulse acquisition sequence in aset of multi-pulse acquisition sequences according to FIG. 5A, 5B, or 5Cmay include a substantive difference between an initial preparatorypulse and a subsequent depth profiling pulse in the sequence. Also, insome embodiments, at least one of, and up to all of, the subsequentdepth profiling pulses in an individual multi-pulse acquisition sequence(within a set of multi-pulse acquisition sequences) may comprise asubstantive difference between the preparatory and subsequent pulses.

FIG. 5A, 5B, or 5C each illustrate a set of acquisitions comprising twoacquisitions, wherein each acquisition comprises two transmit pulses andtwo receive operations. It will be appreciated that sets may compriseadditional acquisitions, and that acquisitions may comprise additionalpulses. The illustrated depth profiling subsequent pulses may compriseone or more ordered subsequent pulses following the preparatory pulses,each ordered subsequent pulse having a pulse moment or maximumexcitation depth, and wherein a pulse moment or maximum excitation depthof an ordered subsequent pulse in at least one of the acquisitionsequences in a set may be substantially different from a pulse moment ofthe same ordered subsequent pulse in at least one other of theacquisition sequences in the set. For example, if an acquisitioncomprises three subsequent pulses including a first, a second, and athird ordered subsequent pulse, the first, second or third subsequentpulse may be substantially different from a same ordered first, secondor third subsequent pulse in at least one other of the acquisitionsequences in the set.

In some embodiments, acquisition schemes disclosed herein may bereferred to as “Crush Recovery” (CR) sequences. In a CR acquisitionscheme, an individual acquisition sequence may comprise transmitting twopulses separated by an adjustable delay time τ_(d). The FID signalfollowing the subsequent pulse (“FID2”) may be recorded; the FIDfollowing the preparatory pulse (“FID1) may also be recorded. A singledelay time CR data set may be comprised of N individual acquisitionsequences wherein I(t) and f(t) for the initial preparatory pulses arefixed, the pulse moments q₂ for the subsequent pulses are varied betweenindividual acquisitions with index i, and the delay time τ_(d) remainsfixed. A complete CR dataset may be comprised of M multiple individualdelay time datasets of index j between which the value of τ_(d) isvaried. A complete CR dataset for a particular fixed preparatory pulsemay comprise a multitude of FID2 signals recorded as a function of timefor varying values of q₂ and τ_(d). It will be appreciated thatapparatus according to FIG. 2 may be configured to gather such datasets, and methods may be performed comprising sequences of pulsetransmit and receive operations effective to gather such data sets. Suchmethods may include, inter alia, the use of on-resonance, composite, oradiabatic preparatory pulses, the use of substantially identicalpreparatory pulses with different subsequent pulses, and/or subsequentpulses with maximum excitation depths that may be substantively smallerthan the maximum excitation depth of the preparatory pulses.

In the preceding CR embodiment, the preparatory pulse may be referred toas the “crush” pulse and the subsequent pulse may be referred to as the“depth-profiling” pulse. A purpose of the crush pulse is to negate,substantially mitigate, or invert signals present in the subsequent FIDthat are associated with the subsurface longitudinal magnetization stateexisting prior to application of the crush pulse. A purpose of thedepth-profiling pulse is to detect, with sensitivity as a function ofdepth, the component of the longitudinal that has recovered during thedelay time.

In the case of an on-resonance crush pulse, the crush pulse maytypically have a substantively higher pulse moment and greater maximumexcitation depth than the subsequent pulse. Thus, this preparatory pulseinduces large tip angles within the same subsurface volumes where thesubsequent depth-profiling pulse induces significant amplitude tipangles. Specifically, within volumes sampled by the subsequent pulse,the crush pulse creates large tip angles that may include multiplecomplete rotations (i.e. rotations greater than 360 degrees). Thus theorientation of the magnetization immediately after the pulse may show ahigh degree of spatial variability ranging from 0 to 360 degrees over asmall spatial scale. Because the subsurface tip angles produced by theapplication of the preparatory pulse are poorly correlated spatiallywithin the shallower volumes sampled by the subsequent pulse, theinitial longitudinal magnetization is effectively crushed andcontributes little coherent energy to the subsequent FID signal excitedby the subsequent pulse. As a result, the magnetization state prior tothe application of the subsequent pulse primarily reflects the componentof the longitudinal magnetization that has been subject to T₁ recoveryprior to application of the subsequent pulse.

In the case of an adiabatic or composite crush pulse, values of I(t),φ(t), and f(t) may be selected such that the pulse produces tip anglenear 90 degrees so as to minimize the longitudinal magnetization over awider range of depths than an on-resonance pulse. Because the crushpulse has also a greater investigation depth than the on-resonancedepth-profiling pulse, the crush pulse minimizes the longitudinalmagnetization over the same range of depths where the depth-profilingpulse induces spatially coherent and significant amplitude tip angles.Thus, the initial longitudinal magnetization is effectively crushed andcontributes little coherent energy to the subsequent FID signal excitedby the subsequent pulse. As a result, the magnetization state prior tothe application of the subsequent pulse primarily reflects the componentof the longitudinal magnetization that has been subject to T₁ recoveryprior to application of the subsequent pulse. In other embodiments,values of I(t), φ(t), and f(t) may be selected such that the pulseproduces tip angles near 180 degrees so as to invert the longitudinalmagnetization over the range of depths where the depth-profile pulseproduces spatially coherent and significant amplitude tip angles.

Varying the value of q₂ for the subsequent depth-profiling pulse betweensingle acquisitions provides sensitivity to the recovered magnetizationas a function of depth and spatial location. Varying the value of τ_(d)between single delay time acquisitions provides sensitivity to the T₁recovery process over time. In some embodiments, a complete CR datasetcan be acquired for more than one value of q₁. In other embodiments,identical acquisitions may be repeated and combined to improve thesignal to noise ratio.

To implement the acquisition sequences described herein, NMR measurementmethods and apparatus according to this disclosure may arbitrarily andindependently control the pulse moment q of transmitted pulses. In someembodiments, the value of q may be varied by changing the duration oftwo pulses independently (i.e., the value of q₂ can be made smaller thanthe value of q₁ by shortening the duration of the subsequent pulse).Changing the duration of the pulse, however, changes the effectivebandwidth. Thus, in some embodiments, the value of q may instead bechanged by varying the current I(t) passed through the surface coil(i.e., the value of q₂ can be made smaller than the value of q₁ byreducing the current passed through the coil for the subsequent pulse).Alternatively, both the pulse duration and current can be variedtogether to control the effective value of q. Methods and apparatusaccording to this disclosure may also be useful to dynamically changethe value of I(t) and/or pulse durations to implement effectiveadiabatic or composite pulses.

To implement the acquisition sequences described herein, NMR measurementmethods and apparatus according to this disclosure may arbitrarily andindependently control the current amplitude I(t) of the transmittedpulses. A number of embodiments may be effective to control the currentthat is passed through the surface coil for each pulse independently;such embodiments may also allow the amplitude of a single pulse to bedynamically varied. In some embodiments, the pulse current may besupplied by switching voltage from one or more DC power supplies with afixed bus voltage. In such embodiments, two or more separate supplieswith different and independent bus voltages can used to supplyingdriving voltage for the two different pulses, thus producing pulses withdifferent amounts of current. Alternatively if there is a single DCpower supply, the duty cycle of the AC (Larmor frequency) switchedcurrent from the DC supply can be varied between pulses or dynamicallyduring a single pulse to decrease or increase the total rms current forthe pulses.

In some embodiments, the current between pulses may be controlled orchanged dynamically during a single pulse, by adjusting the impedance ofthe transmitting device and/or the transmitting coil or coils, betweenthe two pulses. In such embodiments the impedance of the transmitterand/or the coil may be adjusted by adding or subtracting resistive orreactive electronics in the transmitter-coil circuit.

In some embodiments, the current between pulses may be controlled orchanged dynamically during a single pulse, by adjusting the differencebetween the resonant frequency of the coil and the frequency of thedriving voltage. As the difference between the driving voltage frequencyand the coil resonant frequency increase, the current on the coil willdecrease. This approach may be particularly useful for controlling thefunctions I(t) and f(t) for an adiabatic pulse, where it is oftenrequired that the amplitude of I(t) be small when the offset betweenf(t) and the Larmor frequency f₀ is large.

In some embodiments, the effective pulse moment between two pulses maybe controlled by transmitting on two different coils. In this embodimentthe large pulse moment of the preparatory pulse is achieved bytransmitting on a coil with low impedance and/or a larger number ofturns, and the smaller pulse moment of the subsequent pulse is achievedby transmitting on a coil with higher impedance and/or smaller number ofturns.

In some embodiments, the effective pulse moment difference between thepreparatory and subsequent pulses may be controlled by using separatetransmitters to generate the preparatory and subsequent pulses.

Disclosed methods to dynamically control and vary the amplitude of asignal pulse or to control and vary the relative amplitude of at leasttwo pulses in a multi-pulse sequence may be useful in the field ofgeophysical surface NMR for measurements different from those describedabove. For example, some acquisitions may use a single adiabatic pulsewhere I(t) is dynamically varied. A single adiabatic pulse may beselected to provide excitation of fluids in the subsurface over a widerrange of depths than an on-resonance pulse and thus improved signaldetection. As another example, a spin-echo pulse sequence may beacquired in which a preparatory excitation pulse has half the amplitudeof a subsequent refocusing pulse, so that the subsequent pulse providestwice the effective tip angle as the preparatory pulse. It may bepreferable to achieve a double of tip angle by adjusting the relativeamplitude of the excitation and refocusing pulses; instead adjustingtheir relative duration would change the effective bandwidth of the twopulses.

In some embodiments, the phase of the transmitted pulses may becontrolled in order to eliminate particular signal artifacts that areundesired. Specifically for embodiments of the CR acquisition scheme,signal artifacts that are not associated with the FID2 signal that aregenerated by the subsequent depth-profiling pulse may be eliminated.These artifacts can potentially include NMR or non-NMR signals thatshare phase coherence with the transmitted pulses. Specifically, for theCR sequence, artifacts associated with residual transverse magnetizationfrom the preparatory pulse and non-NMR artifacts associated with thesubsequent pulse may be effectively cancelled. A phase cycling strategycan be implemented to mitigate such artifacts.

In some embodiments of phase cycling for the CR sequence, acquisitionsin which the phase of the pulses are varied, but all other parametersare kept identical may be repeated and combined to improve signal tonoise and to suppress artifacts. To achieve artifact suppression byphase cycling for a single CR acquisition, two identical acquisitionsmay be acquired, referred to as A and B. The phase of the preparatorypulse in both sequences may be fixed between acquisition A and B; thesubsequent pulse may have a value of φ₂ in acquisition A and a value ofφ₂+180° in acquisition B. Data for the two acquisitions may then belinearly combined by subtracting the data for acquisition B from thedata for acquisition A. The result is that undesired artifacts that haveconstant phase between both acquisitions are cancelled, including (i)NMR signals representing residual transverse magnetization from thepreparatory pulse and (ii) non-NMR signals that are associated with thehardware artifacts after the subsequent pulse. NMR signals that have a180° phase shift between the acquisitions are preserved, specificallythe component of the FID2 signal associated with recovered longitudinalmagnetization.

Some embodiments may use more than two pulses to allow detection of NMRspin echo signals used to further estimate the T₂ relaxation time, andits covariance with T₁ and T₂*, as a function of subsurface position. Inone such embodiment, that may be termed “crush-recovery spin-echo”(CRSE), a set of multi-pulse acquisition sequences may comprise acollection of multi-pulse acquisition sequences, wherein at least threepulses are used in each multi-pulse acquisition sequence. Thepreparatory crushing pulse may be on-resonance, adiabatic, or compositeand at least two on-resonance subsequent pulses may have values of q₂,q₃, where the value of q₃ is 0.75 to 2.5 times the value of q₂. A secondpulse may be referred to as the “depth sensitive pulse” and a thirdpulse may be referred to as the “refocusing pulse”. The delay timebetween the preparatory and second pulse may be called τ_(d1), and thedelay time between the second and third pulse may be called τ_(d2). Inat least one of the multi-pulse acquisition sequences in the set, theproperties of the crushing pulse are constant, the value of τ_(d1) isconstant, and maximum excitation depth of the second pulse issubstantively less than that of the preparatory pulse. In such anembodiment, the preparatory pulse may act to crush the magnetizationwithin a range of subsurface depths where later pulses providesensitivity to NMR FID and spin echo signals. Spin echo signals may beobserved following the third (refocusing) pulse.

FIG. 6 illustrates a NMR acquisition in which additional refocusingpulses may be transmitted in an acquisition sequence and a train of spinecho signals may be recorded between the refocusing pulses. Such anembodiment may be referred to as a Crush-RecoveryCarr-Purcell-Meiboom-Gill (CRCPMG) sequence. FIG. 6 may generally beunderstood with reference to FIG. 5A, above. FIG. comprises anacquisition i 600 and an acquisition i+1 610, wherein acquisition i 600comprises transmit operations 601 and 603, as well as refocusing pulses605, and receive operations 602 and 604, as well as receive operationsfor spin echo signals 606. Acquisition i+1 610 comprises transmitoperations 611 and 613, as well as refocusing pulses analogous torefocusing pulses 605 in acquisition i, and receive operations 612 and614, as well as receive operations for spin echo signals as illustrated.In FIG. 6, the preparatory pulses 601 and 611 and depth profiling pulses603 and 613 may be according to any of FIG. 5A, 5B, or 5C.

In embodiments according to FIG. 6, the refocusing pulses 605 in asingle acquisition such as acquisition i 600 may have similar pulsemoments q₃. The time delays between each refocusing pulse τ_(d2) may besimilar for the single acquisition and between acquisitions, with variedvalues of q₂ and q₃ between acquisitions, that is, varied pulse momentsfor depth profiling pulses 603 and 613, and varied pulse moments forrefocusing pulses 605 and the refocusing pulses of acquisition i+1 610.In some embodiments, the time delay between a depth profiling pulse 603and a first refocusing pulse 605 may be approximately 0.5* τ_(d2). Acomplete CRCPMG dataset may comprise multiple acquisitions between whichthe value of q2, q3, τ_(d1), and τ_(d2) are varied.

Processing of Surface NMR Signals

Various processing approaches can be used to process data acquiredfollowing the above embodiments to estimate the spatial variation influid content and relaxation times in the subsurface. The below outlinedapproaches to estimate fluid content, T₂*, and T₁ in the subsurface aremade possible because of two unique characteristics of theaforementioned CR acquisition scheme: (i) the initial longitudinalmagnetization is effectively crushed prior to application of thesubsequent pulse, and (ii) the initial conditions prior to applicationof the depth-sampling pulse are consistent across any set of singleacquisitions for which the properties of the preparatory pulse and τ_(d)are fixed. As a result, it is possible to use a standard NMRmathematical inversion kernel described in prior art to isolate thesignal associated with the recovered longitudinal magnetization as afunction of depth.

In some embodiments, a complete CR dataset can be processed in severalstages, as shown in FIG. 7 and FIG. 8. FIG. 7 and FIG. 8 representoperations which may be performed in accordance with example methods,processing operations and/or functional modules which may be implementedin a computing device, and instructions which may be recorded on acomputer readable medium.

Referring to FIG. 7, the complete CR dataset 701 may comprise acollection of voltage signals V(t, τ_(d), q₂), such as 702, 703, and anyother voltage signals, with M values of τ_(d). The CR dataset 701 may beseparated into M single delay-time datasets V(t, τ_(d)=τ_(d,j), q₂) 702,703, etc. A mathematical spatial inversion may be performed for each jthdataset at blocks 704, 705, etc., to derive scaled position ordepth-separated signal S(t, τ_(d)=τ_(d,j), z=z_(k)) represented by dataitems 706, 707, etc., for each depth layer z_(k) in the subsurface. Herethe S(t, τ_(d)=ττ_(d,j), z=z_(k)) signals 708 represents the FID2response associated with the component of the longitudinal magnetizationthat has recovered by T₁ over a delay time of τ_(d,j) at a depthinterval z_(k). The S(t, τ_(d,j), z) signals 708 may also be scaledduring the inversion so that they reflect the volumetric water contentat each depth. The mathematical inversion may alternatively operate intwo or three spatial dimensions to estimate the scaled signals as afunction of the location of finite volume elements.

In some embodiments, the aforementioned mathematical spatial inversionmay follow a linear inversion using a standard forward modeling kernelK(r,q) where r is a subsurface position (or K(z,q) in 1D) which is usedfor standard NMR single-pulse FID measurements. It should be noted thatthe use of the standard kernel is possible at least in part because theinitial conditions prior to the application of the subsequent pulse areidentical for all acquisition sequences where q₁ and τ_(d) are fixed.Attempting to use the same approach to invert data acquired using a PSRsequence may produce erroneous results because the initial conditionsprior to the application of the subsequent pulse may vary as the q-valueof the subsequent pulse varies (because the q-value of the preparatorypulse also changes). Other signal conditioning processes including theapplication of noise cancellation or phase compensation may be appliedat any stage before or during the spatial inversion step.

In some embodiments, a spatial inversion of a CRSE or CRCPMG dataset mayfollow a similar procedure as was outlined above for the CR dataset,wherein the forward model kernel for the FID signal is replaced by aforward model kernel for a spin-echo signal. The output of such amathematical inversion may be spin echo signals S(z, t, τ_(d1), τ_(d2))estimated as a function of depth.

Returning to the CR dataset, given the spatially inverted FID2 signalsfor a given depth S(t, τ_(d)) there are various approaches that can beused to estimate the relaxation times, multi-exponential distributionsof relaxation times, and the covariance of the relaxation times. Variousembodiments for estimating T₂* and T₁ from a crush recovery dataset areillustrated in a schematic flow chart in FIG. 8.

In some embodiments, the S(t, τ_(d)=τ_(d,j)) signal 801 for each jthdelay time at each depth may be processed using a 1-dimensional Laplaceinversion 802 to determine a T₂* distribution. Each T₂* distribution isthen subdivided into bins such as 803 and 804, classifying short T₂* 803or long T₂* 804 signals according to a specified cut-off value of T₂*.For each delay time, the integrated amplitude of the signal iscalculated for the short T₂* bin S_(A)(τ_(d)) and the long T₂* binS_(B)(τ_(d)). The resulting S_(A)(τ_(d)) and S_(B)(τ_(d)) curves may beprocessed separately using a single-exponential fit or Laplace inversionin blocks 805 and 806 to determine the fluid volume and T₁characteristics of NMR signals having short T₂* values 807 separatelyfrom the fluid volume and T₁ characteristics of NMR signals having longT₂* values 808. Alternatively, the T₂* distributions can be separatedinto more than two bins (e.g. three bins to independently classifysignals with short, intermediate, and long T₂* decay times, or anyarbitrary number of subdivided bins).

In some embodiments, a finite number of decay time bins equal to orsmaller than the total number of delay time datasets may be specified,and the S(t, τ_(d)) signals for which τ_(d) is within each specified binrange may be combined by linear averaging. For example a signal S_(C)(t)may be computed by averaging signals with a given range of short τ_(d)at block 811 and a subsequent signal S_(D)(t) may be computed byaveraging the signals with a given range of long delay times at block812. The resulting S_(C)(τ_(d)) and S_(D)(τ_(d)) curves may then beprocessed separately using a single-exponential fit or Laplace inversionat blocks 813, 814 to determine the fluid volume and T₂* characteristicsof NMR signals having short T₁ values 815 separately from the fluidvolume and T₂* characteristics of NMR signals having long T₁ 816.Alternatively, the S(t, τ_(d)) signals may be divided into any number ofbins less than the total number of delay times acquired in the completedataset.

In some embodiments, the S(t, τ_(d)) signals can be processed tosimultaneously estimate the a two-dimensional distribution of T₂* versusT₁. Generally, the S(t, τ_(d)) can be represented by the followingfunction assuming a multi-exponential relaxation behavior:

${S\left( {t,\tau_{d}} \right)}{\int{\int{{w\left( {T_{2}^{*},T_{1}} \right)}{^{- \frac{t}{T_{2}^{*}}}\left( {1 - ^{- \frac{\tau_{d}}{T_{1}}}} \right)}{T_{2}}{T_{1}}}}}$

In some embodiments, a two-dimensional Laplace inversion of the S(t,τ_(d)) can be used at block 821 to estimate the two-dimensionaldistribution and covariance of T₂* and T₁ at a given depth, shown atblock 822. An advantage of such embodiments is that it is possible toimpose constraints on the covariance of T₂* and T₁. For example aconstraint can be exercised that the value of T₁ must be greater thanthe value of T₂*, as is known to be required by NMR physics. Further, itis possible to specify a bound on the value of T₁, the value of T₂*, oron the ratio of T₁ to T₂*, which can improve the stability of theinversion. Specifying bounds in the manner also enables dense samplingand precision of the T₂* decay process (set by the dense data samplingrate of the NMR voltage recording) to improve that the temporalresolution of the T₁ decay process, which is sparsely sampled in time(given a finite number of τ_(d) values).

In some embodiments, data may be acquired using a CRCPMG sequence andused to estimate the two-dimensional covariance distribution of T₁ andT₂. In such an embodiment the spatially inverted data S(t, τ_(d1)) for afixed value of τ_(d2) may first be analyzed to determine the amplitudeof each spin echo signal S_(echo) recorded at the center time t betweenrefocusing pulses and for each value of τ_(d1) in the full set ofacquisitions. A two-dimensional Laplace inversion of the resultingdataset S_(echo)(t, τ_(d1)) may then be used to estimate thetwo-dimensional distribution and covariance of T₂ and T₁ at a givendepth. The decay time T_(D) associated with diffusion of the fluid is afunction of the delay time between refocusing pulses (τ_(d2)). Thus ifacquisitions with varied values of τ_(d2) are included in the set, theresulting dataset S_(echo)(t, τ_(d1), τ_(d2),) may be used with athree-dimensional Laplace inversion to determine a three-dimensionalcovariance distribution of T₁ T₂ and T_(D). T₁, T₂*, T₂, T_(D), andtheir spatial distribution in the subsurface derived by the abovemethods may be used to estimate other properties, including fluid,geologic, hydrogeologic, mineralogic, or biogeologic properties. Forexample T₁ and T₂ can be highly sensitive to fluid viscosity, pore size,permeability, and surface mineralogy and so can be used to estimatethese properties. Also T_(D), T₂*, and the ratio of T₂*:T₁ or T₂:T₁ maybe sensitive to the magnetic properties of the formation and diffusioncoefficient of the fluid.

In some embodiments, surface NMR apparatus and subsurfacecharacterization techniques provided herein may be applied to image NMRproperties at positions in the subsurface. In some embodiments, NMRapparatus and subsurface characterization techniques provided herein maybe applied to image and estimate NMR relaxation times at positions inthe subsurface, which can be related to subsurface properties ofinterest, including pore size and permeability. In some embodiments, NMRapparatus and subsurface characterization techniques provided herein maybe applied to estimate relaxation times and to provide improvedestimation and imaging of the T₁ relaxation at positions in thesubsurface. In some embodiments, NMR apparatus and subsurfacecharacterization techniques provided herein may be applied to provideimproved estimation and imaging of the covariance of more than onerelaxation time at positions in the subsurface. In some embodiments, NMRapparatus and subsurface characterization techniques provided herein maybe applied to provide estimation of more than one relaxation time andtheir covariance as a function of depth from surface NMR measurements.

There is little distinction left between hardware and softwareimplementations of aspects of systems; the use of hardware or softwareis generally (but not always) a design choice representing cost vs.efficiency tradeoffs. There are various vehicles by which processesand/or systems and/or other technologies described herein can beeffected (e.g., hardware, software, and/or firmware), and that thepreferred vehicle may vary with the context in which the processesand/or systems and/or other technologies are deployed. For example, ifan implementer determines that speed and accuracy are paramount, theimplementer may opt for a mainly hardware and/or firmware vehicle; ifflexibility is paramount, the implementer may opt for a mainly softwareimplementation; or, yet again alternatively, the implementer may opt forsome combination of hardware, software, and/or firmware.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof. In one embodiment,several portions of the subject matter described herein may beimplemented via Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs), digital signal processors (DSPs), orother integrated formats. However, those skilled in the art willrecognize that some aspects of the embodiments disclosed herein, inwhole or in part, can be equivalently implemented in integratedcircuits, as one or more computer programs running on one or morecomputers (e.g., as one or more programs running on one or more computersystems), as one or more programs running on one or more processors(e.g., as one or more programs running on one or more microprocessors),as firmware, or as virtually any combination thereof, and that designingthe circuitry and/or writing the code for the software and or firmwarewould be within the skill of one skilled in the art in light of thisdisclosure. In addition, those skilled in the art will appreciate thatthe mechanisms of the subject matter described herein are capable ofbeing distributed as a program product in a variety of forms, and thatan illustrative embodiment of the subject matter described hereinapplies regardless of the particular type of signal bearing medium usedto actually carry out the distribution. Examples of a signal bearingmedium include, but are not limited to, the following: a recordable typemedium such as a floppy disk, a hard disk drive, a Compact Disc (CD), aDigital Video Disk (DVD), a digital tape, a computer memory, etc.; and atransmission type medium such as a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.).

Those skilled in the art will recognize that it is common within the artto describe devices and/or processes in the fashion set forth herein,and thereafter use engineering practices to integrate such describeddevices and/or processes into data processing systems. That is, at leasta portion of the devices and/or processes described herein can beintegrated into a data processing system via a reasonable amount ofexperimentation. Those having skill in the art will recognize that atypical data processing system generally includes one or more of asystem unit housing, a video display device, a memory such as volatileand non-volatile memory, processors such as microprocessors and digitalsignal processors, computational entities such as operating systems,drivers, graphical user interfaces, and applications programs, one ormore interaction devices, such as a touch pad or screen, and/or controlsystems including feedback loops and control motors (e.g., feedback forsensing position and/or velocity; control motors for moving and/oradjusting components and/or quantities). A typical data processingsystem may be implemented utilizing any suitable commercially availablecomponents, such as those typically found in datacomputing/communication and/or network computing/communication systems.The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, different othercomponents. It is to be understood that such depicted architectures aremerely exemplary, and that in fact many other architectures can beimplemented which achieve the same functionality. In a conceptual sense,any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermediate components. Likewise, any two componentsso associated can also be viewed as being “operably connected”, or“operably coupled”, to each other to achieve the desired functionality,and any two components capable of being so associated can also be viewedas being “operably couplable”, to each other to achieve the desiredfunctionality. Specific examples of operably couplable include but arenot limited to physically couplable, physically interacting, wirelesslyinteracting, and/or logically interacting components.

With respect to the use of plural and/or singular terms herein, thosehaving skill in the art can translate from the plural to the singularand/or from the singular to the plural as is appropriate to the contextand/or application. The various singular/plural permutations may beexpressly set forth herein for sake of clarity. It will be understood bythose within the art that, in general, terms used herein, and especiallyin the appended claims (e.g., bodies of the appended claims) aregenerally intended as “open” terms (e.g., the term “including” should beinterpreted as “including but not limited to,” the term “having” shouldbe interpreted as “having at least,” the term “includes” should beinterpreted as “includes but is not limited to,” etc.). It will befurther understood by those within the art that if a specific number ofan introduced claim recitation is intended, such an intent will beexplicitly recited in the claim, and in the absence of such recitationno such intent is present. For example, as an aid to understanding, thefollowing appended claims may contain usage of the introductory phrases“at least one” and “one or more” to introduce claim recitations.However, the use of such phrases should not be construed to imply thatthe introduction of a claim recitation by the indefinite articles “a” or“an” limits any particular claim containing such introduced claimrecitation to inventions containing only one such recitation, even whenthe same claim includes the introductory phrases “one or more” or “atleast one” and indefinite articles such as “a” or “an” (e.g., “a” and/or“an” should typically be interpreted to mean “at least one” or “one ormore”); the same holds true for the use of definite articles used tointroduce claim recitations. In addition, even if a specific number ofan introduced claim recitation is explicitly recited, those skilled inthe art will recognize that such recitation should typically beinterpreted to mean at least the recited number (e.g., the barerecitation of “two recitations,” without other modifiers, typicallymeans at least two recitations, or two or more recitations).Furthermore, in those instances where a convention analogous to “atleast one of A, B, and C, etc.” is used, in general such a constructionis intended in the sense one having skill in the art would understandthe convention (e.g., “a system having at least one of A, B, and C”would include but not be limited to systems that have A alone, B alone,C alone, A and B together, A and C together, B and C together, and/or A,B, and C together, etc.). In those instances where a conventionanalogous to “at least one of A, B, or C, etc.” is used, in general sucha construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, or C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

While various embodiments have been disclosed herein, other aspects andembodiments will be apparent to those skilled in art.

1. A surface Nuclear Magnetic Resonance (NMR) measurement methodcomprising: generating a set of multi-pulse acquisition sequences on oneor more transmitting coils, each multi-pulse acquisition sequencecomprising: a preparatory pulse with a first pulse moment or maximumexcitation depth, wherein said preparatory pulse is substantiallyidentical in each of the multi-pulse acquisition sequences in the set;and one or more ordered subsequent pulses following the preparatorypulse, each ordered subsequent pulse having a pulse moment, and whereina pulse moment of a subsequent pulse in at least one of the multi-pulseacquisition sequences in the set is substantially different from a pulsemoment of a same ordered subsequent pulse in at least one other of themulti-pulse acquisition sequences in the set; and recording resultingNMR signals on a receiving device.
 2. The method of claim 1, wherein thepreparatory pulse is an on-resonance pulse, an adiabatic pulse, or acomposite pulse.
 3. The method of claim 1 wherein a pulse moment ormaximum excitation depth of a subsequent pulse in at least one of themulti-pulse acquisition sequences in the set is substantively less thana pulse moment or maximum excitation depth of a preparatory pulse insaid at least one multi-pulse acquisition sequence.
 4. The method ofclaim 1, further comprising controlling and varying the amplitude of atleast one pulse in said at least one multi-pulse acquisition sequence toproduce the difference in pulse moment or maximum excitation depth. 5.The method of claim 1, further comprising dynamically controlling andvarying the amplitude of at least one preparatory pulse in the setduring the at least one preparatory pulse.
 6. The method of claim 1,further comprising controlling the amplitude of at least one pulse inthe set by: adjusting, in a surface NMR acquisition apparatus, a dutycycle of an Alternating Current (AC) switched current from a DirectCurrent (DC) power supply; switching a transmitting circuit in a surfaceNMR acquisition apparatus, between two or more power supplies withdifferent bus voltages; switching a resistive element to selectivelycouple the resistive element within a transmitting circuit in a surfaceNMR acquisition apparatus; adjusting, in a surface NMR acquisitionapparatus, an offset between a frequency of a driving signal and aresonant frequency of a transmitting coil; switching between two or moretransmitter units in a surface NMR acquisition apparatus; or switchingbetween two or more transmitting coils in a surface NMR acquisitionapparatus.
 7. The method of claim 1, wherein the pulse moment of thesame ordered subsequent pulse is varied between multi-pulse acquisitionsequences to provide sensitivity to variation in NMR properties as afunction of depth or distance from the transmission source.
 8. Themethod of claim 1, further comprising generating two or more sets ofmulti-pulse acquisition sequences, and varying delay time between pulseswithin multi-pulse acquisition sequences from set to set to providesensitivity to NMR decay times.
 9. The method of claim 1, furthercomprising generating two or more sets of multi-pulse acquisitionsequences, and wherein the only difference between at least two sets ofmulti-pulse acquisition sequences is the phase of at least one orderedsubsequent pulse in the multi-pulse acquisitions.
 10. The method ofclaim 9, further comprising linearly combining recorded NMR signals fromthe more than one set of multi-pulse acquisitions to separate undesiredsignals from desired signals.
 11. The method of claim 1, wherein atleast one of the multi-pulse acquisition sequences comprises two or moreordered subsequent pulses to enable measurement of a spin echo signal ortrain of spin echo signals.
 12. The method of claim 1, furthercomprising using recorded NMR signals to estimate information about therelaxation times T₁ and T₂*, T₂ and T_(D) as a function of position. 13.The method of claim 1, further comprising using recorded NMR signals toestimate one-dimensional distributions, two-dimensional covariancedistributions, or higher-dimensional covariance distributions of T₁, T₂,T₂*, and T_(D) as a function of position.
 14. The method of claim 13,further comprising using one or more of the estimated distributions toestimate a physical property of a subsurface Earth or an engineeredmaterial, the physical property including one or more of a geologic,hydrogeologic, mineralogic, chemical, fluid, biogeologic, orgeotechnical property.
 15. A surface NMR measurement apparatusconfigured to generate a set of multi-pulse acquisition sequences, eachmulti-pulse acquisition sequence comprising: a controller; and an NMRsensor; wherein the controller is configured to cause the NMR sensor togenerate a set of multi-pulse acquisition sequences, each multi-pulseacquisition sequence comprising: a preparatory pulse with a first pulsemoment or maximum excitation depth, wherein said preparatory pulse issubstantially the same in each of the multi-pulse acquisition sequencesin the set; and one or more ordered subsequent pulses following thepreparatory pulse, each ordered subsequent pulse having a pulse moment,and wherein a pulse moment of a subsequent pulse in at least one of themulti-pulse acquisition sequences in the set is substantially differentfrom a pulse moment of a same ordered subsequent pulse in at least oneother of the multi-pulse acquisition sequences in the set; and arecording device configured to record resulting NMR signals.